Experimental Investigation on Drying of Forest Biomass Particles in a Mechanically Stirred Fluidized Bed

Abstract

This chapter reflects a review of the results obtained in several investigations on the fluidization process of wet biomass particles in a mechanically stirred fluidized bed equipment. For the experimental purposes, an experimental equipment with a drying column of 300 mm in diameter is used. Using the Ergun equation, the fluodynamic behavior of the bed is analyzed to obtain, from the measurements of pressure drops in the bed and imposed velocities, the specific gas-particle contact surface; such interfacial surface varies between 5758 and 7317 m2 m–3 for dry particles and between 2774 and 4444 m2 m–3 for high humidity particles. Subsequently, the phenomena of heat and mass transfer by convection between the fluidizing gas and the biomass particles during the drying process are studied. The gas-particle heat and mass transfer coefficients are determined, considering stirrer rotation speeds between 1 and 2 rev s–1. The convective coefficients vary between 13 and 25.7 W m–2 K–1 for heat transfer and between 6 x 10–3 and 20 x 10–3 m s–1 for mass transfer; thus, correlations have been obtained between the Nusselt and Reynolds numbers and between the Sherwood and Reynolds numbers, respectively, valid in the Reynolds number range between 102 and 257.

1. Introduction

Forests and the wood industry’s residues represent an extraordinary source of energy for enterprises and communities located near areas where wood is harvested, and wood byproducts are produced. Currently, there is a clear conviction about the need to make rational use of this energy resource. Therefore, interest in the development of renewable energy studies will continue in the coming years. In the case of biofuels, it is a significant field for applied research.

Among the alternatives for using these resources, there is the possibility of combustion or gasification to generate thermal and/or electrical energy, or the option of producing fertilizer products. The process of densifying wood from forest residues or the wood industry can also be an important alternative due to its low density, low calorific value, and in some cases, high moisture content, which results in high biomass consumption. In industrial processes, the reuse of waste for transformation into byproducts with higher added value, such as particleboard or wood fibers, also generates environmental benefits.

In thermochemical processes such as the combustion of forest biomass, the limitation is the low calorific value of the fuel due to its high moisture content. For this reason, burning them without prior drying requires the use of large volumes of combustion chambers to process the fuel. In this sense, a drying process is important as a preliminary stage to combustion to reduce the volume of the combustion chamber, achieve an adequate combustion temperature, and improve the thermal efficiency of the process.

On the other hand, biomass gasification and pyrolysis processes are normally carried out with low humidity. Thus, for example, according to [1, 2] sawdust gasification in a fluidized bed requires moisture contents of 8–12% and 8.5%, respectively.

In the field of particle board manufacturing, briquettes or pellets require very low levels of humidity. Indeed, the transformation of green wood into particles is done with moisture contents that can vary between 35 and 150% d.b., but the subsequent processes of gluing and pressing the particles require that the moisture be between 5 and 10% to the outer layers and from 2 to 6% for the middle layer. In this context [3], carried out a study on the drying of wood particles in rotary equipment with a humidity of 65% to leave the biomass with a final moisture content of 9–11% d.b., thus allowing hot pressing of the particles for the manufacture of MDF boards. Zabaniotou [4] also studied the drying of forest biomass in rotary equipment but with low initial moisture levels (13% d.b.).

It can then be seen that in all the industrial applications mentioned, the humidity values required for the various transformation processes of the residual biomass are well below the humidity with which it is normally available and that can be 150–170% d.b. It is not always possible to have these residues in a dry state and among the preparatory treatments that are required is the drying of the biomass, which has motivated this research.

Fluidized bed technology has become one of the most successful worldwide. It currently finds applications not only in thermal processes such as combustion, gasification and drying, but also in others on roasters, calciners, classifiers and reactors within the metallurgical, chemical, and pharmaceutical sectors.

In a previous work [5] the authors carried out a thermal study on the drying of biomass particles in a mechanically stirred fluidized bed equipment; the objective of the study was to determine the production rates of forest biomass particles, the evaporation rates, the specific energy consumption, and the thermal efficiency of the drying process. The most important results of this study reveal that the specific energy consumption is 3040 kJ for each kg of water evaporated in the bed, which corresponds to a thermal efficiency of 80%.

In this research the first objective is to experimentally analyze the aerodynamics of the fluidized bed, in order to obtain minimum fluidization velocities, pressure drops in the bed and the specific surface of the gas-particle contact. The second objective is to study the phenomena of heat and mass transfer that occur simultaneously during the drying of the biomass particles, in order to determine the convective coefficients of heat and mass transfer in the contact surface between the biomass particles and the fluidizing gas.

2. Theoretical background

In solid drying processes, momentum, heat, and mass transport phenomena occur simultaneously. The study of these phenomena is important to define aspects of the mechanical and thermal design of a drying equipment. Particularly, in a fluidized bed dryer, the study of the fluid dynamics of the bed and the determination of minimum fluidization velocities and pressure drop in the bed have been the objective of many studies.

In some cases, the problem has been considered as a particle isolated from the rest of the particles; in others, the interaction with other particles is considered (a situation that always occurs in a fluidized bed). It is well known that in fluidized beds with irregular particles, turbulent flow occurs, in which case energy losses due to kinetic effects are more important than losses of viscous origin.

On the other hand, in the thermal design of a fluidized bed dryer, it is important to know the heat and mass transfer coefficients that occur at the particle-gas interface because with them the boundary conditions can be formulated in modeling problems of the drying process. Particularly, during the period of constant drying rate, in which the predominant drying mechanism is convective at the gas-particle interface.

2.1 Transport of momentum in a fluidized bed

In fluidized systems, it is necessary to perform analysis using constitutive equations, which are added to the momentum balance equations.

In the case of flows in porous matrices with low-velocity flows and low Reynolds numbers, the Darcy equation relates the resistive force between the fluid and the porous matrix with the superficial velocity of the fluid. On the other hand, for fluidized beds of large particles, a situation that occurs in a particulate biomass dryer, the resistant force depends on the viscous losses and the kinetic energy losses.

Therefore, in a fluidized bed, the equation that determines the pressure drops, developed by Ergun [6] establishes that:

$$\frac{\mathrm{\Delta }p}{L}=150\frac{{\left(1-\epsilon \right)}^2}{{\epsilon }^3}\frac{{\mu }_{g}U}{{D_p}^2}+1.75\frac{1-\epsilon }{{\epsilon }^3}\frac{\mathit{GU}}{D_p}$$E1

In the case of fluidized beds with irregular particles (non-spherical), the Ergun equation must take into account the sphericity of the particle through the relationship 6/ϕD_p, that represents the specific surface area of the particles S_p for arbitrary particles of similar size and expressed as the contact surface of particles per unit volume of solids.

Therefore, in the case of non-spherical particles, Ergun equation can be rewritten in terms of S_p as follows:

$$\frac{\mathrm{\Delta }p}{L}=150\frac{{\left(1-\epsilon \right)}^2}{{\epsilon }^3}\frac{{\mu }_{g}U}{36}{S_p}^2+1.75\frac{1-\epsilon }{{\epsilon }^3}\frac{\mathit{GU}}{6}{S}_p$$E2

If the superficial velocity U is lower than the minimum fluidization velocity U_mf, the bed remains in its rest condition and Eq. (2) allows determining the specific surface area S_p of the particles contained in the bed. For this, experimental data of the pressure drop as a function of superficial velocity must be available under the condition that U < U_mf.

2.2 Gas-particle convective heat and mass transfer in fluidized bed

For the analysis of heat transfer between a spherical particle and a gas with relative velocity U (spherical liquid drop falling in a gas), in Ranz and Marshall [7] the following dimensionless equation is proposed:

$${\mathit{Nu}}_{\mathit{gp}}=\frac{h_{\mathit{gp}}{D}_p}{k_g}=2.0+0.60{\left(\frac{{\rho }_g{\mathit{UD}}_p}{{\mu }_g}\right)}^{1/2}{\left(\frac{C_g{\mu }_g}{k_g}\right)}^{1/3}$$E3

In the analysis of heat transfer in fluidized beds, particularly at high fluidization velocities and Reynolds numbers, there are dimensionless correlations similar to Eq. (3). For example [8] proposes the following correlation for coarse particles (Re_p > 100) and in a fixed bed condition:

$${\mathit{Nu}}_{\mathit{gp}}=2+1.8{{\mathit{Pr}}_g}^{\mathit{1}/\mathit{3}}{{\mathit{Re}}_p}^{\mathit{1}/2}$$E4

For low values of Reynolds number, this equation presents important deviations in relation to experimental results. However, in such cases, the experimental results correlate well with those predicted by the Kunii and Levenspiel equation, whose fundamental assumption is the existence of a plug flow regime:

$${\mathit{Nu}}_{\mathit{gp}}=0.03{{\mathit{Re}}_p}^{1.3}$$E5

for 0.1 < Re_p < 100, under the assumption of a plug flow.

On the other hand, and in a similar way to what happens with the phenomenon of heat transfer, the analysis of the mass transfer in a forced convection regime between an isolated spherical particle and a gas in relative motion can be carried out using the experimental correlation of [9]:

$${\mathit{Sh}}_{\mathit{gp}}=\frac{k_{\mathit{gp}}{D}_p}{D_v}=2.0+0.60{\left(\frac{{\rho }_g{\mathit{UD}}_p}{{\mu }_g}\right)}^{1/2}{\left(\frac{{\mu }_g}{{\rho }_g{D}_v}\right)}^{1/3}$$E6

for 0.6 < Sc_g < 2.7 and 2 < Re_p < 800.

For fixed beds [7], also reported an expression for the calculation of the Sherwood number for large particles (Re_p > 80) in liquid and gas systems. When applied to gaseous systems, the equation can be written as:

$${\mathit{Sh}}_{\mathit{gp}}=2.0+1.8{\mathit{Re}}_p^{\mathit{1}/\mathit{2}}{\mathit{Sc}}_g^{1/3}$$E7

In analogy with the phenomenon of heat transport, for flow regimes with low Reynolds numbers, Eq. (7) does not adequately predict the value of the Sherwood number and in these cases, it is recommended to use the following equations proposed by Richardson and Szekely [10].

$${\mathit{Sh}}_{\mathit{gp}}=0.374{\mathit{Re}}_p^{\mathit{1.18}}\text{for}0.1<{\mathit{Re}}_p<15$$E8

$${\mathit{Sh}}_{\mathit{gp}}=2.01{\mathit{Re}}_p^{0.5}\text{for}15<{\mathit{Re}}_p<250$$E9

3. Material and methods

3.1 Aerodynamics in an agitated fluidized bed of biomass particles

The experiments were carried out in a laboratory equipment whose main section, the drying chamber, is shown in Figure 1; details of the equipment, which has also been used to carry out the experiment on heat and mass transfer, can be found in Moreno et al. [11]. Figure 2 shows an overview of the equipment.

Figure 1.

Schematic diagram of experimental equipment.

Figure 2.

Overview of the fluidized bed dryer of biomass particles.

To develop the aerodynamic analysis of the fluidized bed, experiments were carried out to determine the pressure drop of the bed as a function of the superficial velocity of the air. The basis weight of the biomass samples was 2.0 kg d.b. The superficial velocity was gradually increased until reaching the U_mf value in order to analyze the bed in its rest condition; the suspended bed condition was also guaranteed, for which the superficial velocities rose above the minimum fluidization velocity.

The d_p particle size varied in the range of 0.51–3.56 mm. The tests were carried out first using particles with equilibrium moisture content (0.15 kg kg⁻¹ d.b.); subsequently, the bed was loaded with wet particles (2.0 kg kg⁻¹ of humidity d.b.), with which the density of the particles varied between 423 and 1044 kg m⁻³.

The experimental velocity data were obtained with a Pitot tube. On the other hand, the pressure drops of the bed were measured with a differential manometer for each superficial velocity tested. In addition, the rotation speed of the mechanical agitator was varied, seeking the best stability condition for the bed of wet particles, since wet biomass particles have a great tendency toward agglomeration as a result of surface forces generated by the water contained in them.

In a fixed bed of biomass particles, the bed porosity ε can be calculated with the values of the density of the particles ρ_p and the density of the static bed ρ_b. Thus,

$$\epsilon =1-\frac{{\rho }_b}{{\rho }_p}$$E10

In order to analyze the quality of the fluidization of biomass particles, prior to the drying tests, the procedure used consists of determining the fraction of particles in the bed that are suspended by the ascending air flow; the fluidization quality index QF is used according to the Eq. (11). Thus, if the bed is completely fluidized, the pressure drop of the bed should be equal to the weight of solids per unit of cross-sectional area of the bed and otherwise the QF index is less than 1.

$$\mathit{QF}=\frac{\mathrm{\Delta }p}{W/A}$$E11

3.2 Fundamentals of gas-particle heat transfer

Regarding the determination of the convective heat transfer coefficient in fluidized beds, in most of the works reported in the literature, the interfacial heat transfer analysis is carried out in batch processes and steady state, where the hot gas enters the bed and is then cooled by making contact with the cold particles. Thus, for a bed layer of thickness dl, the convective coefficient can be represented as:

$$-C_{g}U{\rho }_g\frac{{\mathit{dT}}_g}{\mathit{dl}}=h_{\mathit{gp}}S\left(T_g-T_{p,s}\right)$$E12

which, integrated for a height l in the bed, allows to obtain:

$$ln\frac{T_{g,i}-T_{p,s}}{T_{g,l}-T_{p,s}}=\frac{h_{\mathit{gp}}S}{{\rho }_{g}U{C}_g}l$$E13

where T_g,i and T_g,l are the gas temperature at the inlet and at a height l of the bed.

Representing the first member of Eq. (13) as a function of l, based on the experimental data, then the value of h_gp can be obtained through the slope plotted on a semilogarithmic graph. The slope can be variable if the local coefficient presents variations depending on the position inside the bed.

Eq. (13) has been obtained on the basis of the complete mixing of gas and particles, that is, assuming that the temperature of the particles in the bed is the same at all points, except for a region of the bed close to the distributor. The above is because temperature gradients and equilibrium between gas and particles are reached in this zone, as already reported by [8, 12, 13]. This means that the gas temperature variations must be measured in the area close to the distributor and that the temperature of the particles can be considered equal to that of the gas at the outlet of the bed. Some authors consider that a thermocouple inserted in the bed provides a measurement of the temperature of the solids, which, strictly speaking, is not the case. This experimental model assumes that heat losses to the environment are negligible.

For studies of heat transfer coefficients in drying systems in the period of constant drying rate, it can be assumed that the temperature of the surface particles T_p,s is equal to the wet bulb temperature T_wb of the inlet air [14, 15], since in such a period the product shows a wet surface.

The analysis of the drying curves, obtained in Moreno [16] allows us to conclude that a large part of the process is carried out under a constant temperature regime and at a constant drying rate. In principle, the determination of the heat transfer coefficients should be carried out using Eq. (13). However, this procedure provides a local value of the convective heat transfer coefficient.

For design purposes, it is more appropriate to work with mean values of h_gp. Thus, in an adiabatic regime, the heat balance equation can be written as:

$$-h_{\mathit{fg}}{\rho }_{p,0}\frac{\mathit{dw}}{\mathit{dt}}=h_{\mathit{gp}}{S}_p\mathrm{\Delta }{T}_{\mathit{ml}}$$E14

Thus, the h_gp calculation can be carried out using the equation:

$$h_{\mathit{gp}}=\frac{h_{\mathit{fg}}{\rho }_{p,0}\left(-\frac{\mathit{dw}}{\mathit{dt}}\right)}{S_p\mathrm{\Delta }{T}_{\mathit{ml}}}$$E15

In Eq. (14) the concept of logarithmic-mean temperature difference is introduced, which for its application in this drying process can be assumed that the surface temperature of the particles is equal to the temperature of the wet bulb of the air because the drying was carried out under the condition of constant rate. Thus:

$$∆T_{\mathit{ml}}=\frac{T_{g,i}-T_{g,o}}{ln\left(\frac{T_{g,i}-T_{\mathit{wb}}}{T_{g,o}-T_{\mathit{wb}}}\right)}$$E16

3.3 Fundamentals of gas-particle mass transfer

In analogy with the convective phenomenon of heat transfer between a solid particle and a fluid, which is governed by Newton’s cooling equation, for a drying process the mass transfer between the wet particle and the air that receives the vapor released by solids is governed by a similar equation, that is:

$${\dot{m}}_v=k_{\mathit{gp}}{A}_p\left(c_{v,s}-c_{v,\infty }\right)$$E17

It can be assumed, in analogy with heat transfer, that the moisture concentration in the humid air c_v,∞ of Eq. (17), at a given bed height, is uniform across the cross section of the drying chamber and the transfer of matter is completed in a very small distance above the distributor.

By making a mass balance during the drying process in the constant drying rate period, for a differential fluidized bed element of thickness dl, the mass flow of water vapor at the particle surface, based on Eq. (17), can be determined. Thus:

$$d{\dot{m}}_v=k_{\mathit{gp}}\left(c_{v,s}-c_v\right)\mathit{\text{SAdl}}$$E18

The water vapor flow can be related to the moist content of the moist air through:

$$d{\dot{m}}_v={\dot{m}}_{\mathit{da}}d{w}_a$$E19

Then:

$${\dot{m}}_{\mathit{da}}d{w}_a=k_{\mathit{gp}}\left(c_{v,s}-c_v\right)\mathit{\text{SAdl}}$$E20

If incompressible flow is considered, then:

$${\dot{m}}_{\mathit{da}}{v}_{a}d{c}_v=k_{\mathit{gp}}\left(c_{v,s}-c_v\right)\mathit{\text{SAdl}}$$E21

When Eq. (21) is integrated from a point on the distributor, for a bed height l, the following is obtained:

$$ln\frac{c_{v,s}-c_{v,i}}{c_{v,s}-c_{v,l}}=\frac{k_{\mathit{gp}}\mathit{SA}}{{\dot{m}}_{\mathit{da}}{v}_a}l$$E22

On the other hand, using an average coefficient of k_gp, the mass balance equation for the entire bed can be written as:

$$k_{\mathit{gp}}=\frac{{\dot{m}}_v}{A_p∆c_{\mathit{ml}}}$$E23

where the logarithmic mean difference in moisture concentration is defined as:

$$∆c_{\mathit{ml}}=\frac{c_{v,o}-c_{v,i}}{ln\left(\frac{c_{v,s}-c_{v,i}}{c_{v,s}-c_{v,o}}\right)}$$E24

Since the equation applies to the entire bed, then A_p = S_pV_p and

$$k_{\mathit{gp}}=\frac{{\dot{m}}_v}{S_p{V}_p∆c_{\mathit{ml}}}$$E25

In terms of the drying rate (−dw/dt) Eq. (25) can be written as:

$$k_{\mathit{gp}}=\frac{{\rho }_{p,0}\left(-\frac{\mathit{dw}}{\mathit{dt}}\right)}{S_p\mathrm{\Delta }{c}_{\mathit{ml}}}$$E26

Similarly, to what was assumed in the heat transfer analysis, in determining the surface mass transfer coefficient it was assumed that the concentration of water vapor on the wetted surface of the particles is equal to that of saturated air and evaluated at the wet bulb temperature of humid air [15].

3.4 Experiments on heat and mass transfer

The experimental dryer has a drying chamber with a diameter of 0.3 m. The biomass load, as in the fluodynamic tests, was 2.0 kg d.b., occupying an approximate height of 0.17 m. The mechanical stirrer was built with a vertical shaft and four blades in total.

To analyze the homogeneity of the bed and its temperature, 8 temperature sensors were installed, as shown in Figures 1 and 3, and connected to a Digi-Sense Cole-Parmer Instrument Company multichannel thermometer; it has a resolution of 0.1 K and ± 0.5 K accuracy and an RS-232 output for connection to a PC. Data was collected every 4 s and analyzed using a ScanLink 2.0 software. An additional temperature sensor PT100 was placed at the entrance of the air flow to the dryer to control the operating temperature of the equipment.

Figure 3.

Arrangement of thermocouples to measure temperature inside the bed.

At the bed outlet, a Digi-Sense digital psychrometric digital recorder was used together with ScanLink 2.0 and PCDAC (Cole-Parmer Instrument Company) programs to collect data every 10 s.

The drying experiences were carried out with Pinus radiata sawdust particles. The operating temperature measured at the inlet of the hot air flow to the drying chamber was recorded, as well as the outlet temperature of the gas above the particle bed.

In determining the mean logarithmic difference of Eq. (16) and to avoid the error caused by the heat transferred from the air to the distributor plate, the temperature of the gas at the bed inlet T_g,i was measured at a point just above the air distributor. Thus, was verified that the air temperature, after passing through the distributor, drops sharply when it comes into contact with the particles. Figure 4 shows a schematic diagram of the thermocouples to obtain the axial distribution of temperature in the bed. The homogenization of the temperature is reached at a height lower than 20 mm above the distributor, as shown in Figure 5, which agrees with the analysis of other authors [8, 12] and the experimental results of [13, 17].

Figure 4.

Schematic position of the thermocouples to determine the axial temperature distribution in the bed; N = 0 rev s⁻¹.

Figure 5.

Axial temperature profile inside the bed, corresponding to seven profiles measured with an inlet temperature equal to 150°C.

The physical properties of the gas were evaluated at the mean temperature of the fluid film surrounding the particle, considering that the particle surface temperature is equal to the air wet bulb temperature.

In the heat and mass transfer experiments, three control factors (U, d_p and N) were used. The experiments were carried out, considering each particle with an air velocity within the range in which its fluidization occurs according to the moisture content of the particles. In order to study possible variations of the h_gc and k_gc coefficients, at each level of (d_p-U) the experiments were performed with two rotation speeds of the mechanical bed stirrer. Table 1 shows the 10 trials with their respective levels; the operating temperature was 150°C in all cases.

dp (mm)	U (m s^−1)	N (rev s^−1)	Umf (m s^−1)
0.89	0.71	1	0.46
0.89	0.71	2	0.46
1.44	0.77	1	0.56
1.44	0.77	2	0.56
1.85	0.81	1	0.66
1.85	0.81	2	0.66
2.18	0.82	1	0.80
2.18	0.82	2	0.80
3.56	1.02	1	0.95
3.56	1.02	2	0.95

Table 1.

Experiments for determination of h_gp and k_gp coefficients.

4. Results and discussion

4.1 Bed porosity, specific surface area, and minimum fluidization velocity

Using Eq. (10) and the procedure described in Section 3.1, the porosity of the bed has been determined in the fixed bed condition. The specific surface has been obtained based on the Ergun’s modified equation. The size d_p corresponds to particles obtained by means of ASTM E-11 sieving. Table 2 shows the results on bed porosity and specific surface area of particles.

dp (mm)	ε (m^3 m^−3)	Sp,0 (m^2 m^−3)	Sp (m^2 m^−3)
0.51	0.604	7317	4444
0.89	0.616	6835	3887
1.44	0.618	6440	3457
1.85	0.631	6243	3253
2.18	0.646	6118	3126
3.56	0.697	5758	2774

Table 2.

Fixed bed porosity and specific surface area for dry and wet biomass particles.

In the preliminary tests in an agitated fluidized bed, the range between 0 and 2 rev s⁻¹ has been chosen, to analyze the behavior of the bed in terms of its mobility, depending on the combination of the superficial velocity and agitation speeds parameters. Tests were carried out with a load of 2 kg of biomass particles of 1.44 mm in size and with a moisture content of 2.0 kg kg⁻¹ d.b.

Figure 6 shows the behavior of the pressure drop in the bed as a function of superficial velocity, for a stirred bed with different stirring speeds. With 0.5 rev s⁻¹ (Figure 6a) it could be seen that at a speed of 1.12 m s⁻¹ (point A), the bed opens abruptly giving way to a sudden increase in the air flow through the bed, reaching a velocity of 1.35 m s⁻¹ (point B). The fluidization stabilizes from a velocity of 1.46 m s⁻¹ with a suspension of the particles equivalent to a QF = 0.78.

Figure 6.

Pressure drop across the bed as a function of superficial velocity with different stirring speeds for d_p = 1.44 mm and w = 2.0 kg kg⁻¹ d.b.

By increasing the turning speed to 1 rev s⁻¹ (Figure 6b), the transition from the fixed bed to the fluidized bed is more gradual with a transition speed of 1.18 m s⁻¹ (A) and a QF = 0.88, but then there tends to be a decrease in QF with increasing velocity. This phenomenon is significantly attenuated at higher turning speed and at 2 rev s⁻¹ (Figure 6d) at a superficial velocity of 0.91 m s⁻¹ (A) the transition from a fixed bed to a fluid bed occurs, reaching a QF = 0.95. A notable aspect of these tests was the minimal amount of particle carryover out of the dryer.

Once the objective of having a high-quality fluidized bed was achieved, the minimum fluidization velocity was determined. Figure 7 shows a curve of pressure drop versus superficial velocity obtained with particles with equilibrium moisture and 1.85 mm size for an agitation velocity of 2.0 rev s⁻¹. When carrying out tests with the other particle sizes, it was found that the qualitative behavior was similar, with obvious differences in the velocity values obtained, depending on the particle size, as shown in Table 3.

Figure 7.

Pressure drop in an agitation-fluidized bed for d_p = 1.85 mm and equilibrium moisture content; N = 2.0 rev s⁻¹.

Dry biomass			Wet biomass
dp (mm)	Experimental Umf	Eq. (27)	dp (mm)	Experimental Umf	Eq. (27)
0.89	0.46	0.46	0.89	—	0.78
1.44	0.56	0.58	1.44	0.91	0.99
1.85	0.66	0.66	1.85	1.09	1.11
2.18	0.80	0.75	2.18	1.42	1.25
3.56	0.95	1.10	3.56	1.69	1.80

Table 3.

Variation of the minimum fluidization velocity U_mf in m s⁻¹, in relation to the particle size d_p for dry and wet biomass; N = 2.0 rev s⁻¹.

From the point of view of the quality of the fluidization of wet particles, it is found that mechanical agitation has an important effect when the particles have high moisture contents, taking into account that a bed of wet biomass is impossible to fluidize without mechanical agitation; in the case of low moisture particles, the effect of agitation is less.

The minimum fluidization velocities U_mf were determined in a mechanically shaken fluidized bed with agitation velocity N = 2 rev s⁻¹, for dry and wet biomass particles; it can be observed in Table 3 that with dry biomass, fluidization velocities are smaller.

For the U_mf velocity prediction, a new correlation is proposed based on a procedure reported in [18]. The initial correlation studied fits well with experimental data in the range of small particles. However, with large particle sizes, the prediction of experimental values of U_mf was not successful and therefore the correlation had to be corrected to consider the variation of the U_mf velocity with the particle size. To carry out this correction, a geometric factor (d_p/D₀) was used, where d_p is the particle size obtained by sieving and D₀ is a reference size equal to 1 mm. Thus, the proposed correlation is:

$${\mathit{Re}}_{\mathit{mf}}=\left[{\left({24.8}^2+0.044{\mathit{GaM}}_{\rho }\right)}^{0.5}-24.8\right]{\left(\frac{d_p}{D_0}\right)}^{1/3}$$E27

The prediction of the velocity of minimum fluidization using Eq. (27) as observed in Table 3, it is acceptable; only in two tests the deviations were −12% and +15%.

4.2 Heat and mass transfer

4.2.1 Thermal characterization of the bed of biomass particles

From the point of view of the fluodynamic behavior of the particles in the fluidized bed, it is first important to guarantee the high quality of their suspension, reflected in a high value of the QF index of Eq. (11), as already indicated. From the thermal point of view itself, the high quality of fluidization has been evidenced in a high homogeneity of the bed temperature, according to the records of the eight thermocouples inserted inside the fluidized bed, as shown in Figure 8, which have been obtained during a drying experiment.

Figure 8.

Temperature profile at different points in the bed during biomass drying experiment.

In addition, this excellent fluidization quality has been verified with the high value of the correlation coefficient R² for the drying curves, as will be seen in the drying experiments. Figure 9 shows one of the drying curves obtained and it can be seen that the process is carried out with a constant drying rate, therefore the ideal adjustment curve in this case would be a straight line with a high value for the explanatory variance R².

Figure 9.

Drying curve for biomass particles in an agitated fluidized bed; R² = 0.996.

On the other hand, in order to know the behavior of the biomass during the drying process, specifically in the range of temperatures normally used in dryers with atmospheric air, a thermogravimetric analysis has been carried out.

The experimental tests were carried out in a Cahn 2000 thermogravimetric equipment, 113× system, equipped with a programmable temperature control system.

Figure 10 shows the TG diagram in an inert atmosphere, for two tests carried out with wet and dry biomass. This diagram shows the percentage of residual weight, with respect to the initial weight loaded, as a function of the sample during the test.

Figure 10.

Thermogravimetric (TG) of wet and dry biomass in an inert atmosphere depending on the temperature.

It can be seen in Figure 10, how the absolute loss of volatiles in the wet biomass is less than in the dry one, for having introduced less dry mass into the sample, since part of it was water (moisture). If the relative value were calculated, it would give the same proportion.

Figure 11 shows two curves obtained for the test carried out in an oxidizing atmosphere, showing good reproducibility, which gives a good degree of reliability in the results obtained. The weight variations between the original test and the replica were 5.3%.

Figure 11.

Thermogravimetric (TG) of biomass in an oxidant atmosphere and its replica.

Table 4 contains a summary of the relevant parameters of the thermogravimetric analysis. The maximum rate of devolatilization and combustion is evaluated according to the following expression:

Parameter	Inert atmosphere test	Air atmosphere test
Initial mass loaded (mg)	5.95	6.29
Ash content (%)	3.90	3.90
Initial mass without ash (mg)	5.72	6.04
Weight loss (%) and range 1 of T (°C)	4.03 (21–110°C)	12.24 (21–114°C)
Weight loss (%) and range 2 of T (°C)	64.04 (155–364°C)	55.96 (187–330°C)
Weight loss (%) and range 3 of T (°C)	12.77 (364–800°C)	27.90 (330–450°C)
Temperature of Umáx (1) (°C)	322	295
Maximum rate (1) (g/g h)	3.35	3.26
Temperature of Umax (2) (°C)	574	437
Maximum rate (2) (g/g h)	0.18	1.13

Table 4.

Thermogravimetric parameters derived from TG and DTG curves of forest biomass.

$$U_{\max }=-\frac{1}{m_{\mathit{isc}}}{\left(\frac{\mathit{dm}}{\mathit{dt}}\right)}_{\max }$$E28

where m_isc corresponds to the initial mass of loaded biomass, on an ash-free basis and (dm/dt)_máx represents the maximum slope of the TG curve (mass versus time).

4.2.2 Convective heat transfer coefficient

The values obtained for the heat transfer coefficients are shown in Table 5, for each of the tests defined in Table 1. When using Eq. (15) in the calculation of the convective heat transport coefficient, the drying rate dw/dt shown in Table 5 was introduced, which in turn is obtained from the experimental drying curve of each test (Figure 9). The value of R² indicated in the table corresponds to the correlation coefficient obtained in the fit of the straight line to the experimental data of moisture content of the solids versus time.

dp	Dp	Rep	-dw/dt	R^2	hgp exp	hgp anal	kgp exp	kgp anal
(mm)	(mm)		(kg kg^−1 min^−1)		(W m^−2 K^−1)	(W m^−2 K^−1)	(m s^−1)	(m s^−1)
0.89	2.44	102	0.067	0.99	15.4	13.0	0.010	0.009
0.89	2.44	103	0.0565	0.994	13.0	13.1	0.006	0.009
1.44	2.70	124	0.0553	0.986	13.2	15.0	0.008	0.011
1.44	2.70	124	0.0586	0.997	14.5	15.0	0.014	0.011
1.85	2.84	136	0.064	0.985	15.7	16.1	0.015	0.012
1.85	2.84	134	0.0631	0.996	14.9	15.8	0.015	0.012
2.18	3.13	148	0.0773	0.973	18.2	16.3	0.016	0.012
2.18	3.13	150	0.0645	0.996	14.4	16.5	0.012	0.013
3.56	4.30	256	0.0957	0.985	23.2	23.9	0.020	0.019
3.56	4.30	257	0.0992	0.99	25.7	24.0	0.015	0.019

Table 5.

Convective heat and mass transfer coefficients.

On the other hand, once the values of the heat transfer coefficient were known, in each test the Nusselt number was calculated using the first equality of Eq. (3) and then the correlation between the Nusselt number and the Reynolds number was obtained, which is proposed in Eq. (29). It has been verified that the rotation speed (N) does not influence the convective heat transfer coefficient, since the variations found in the h_gp coefficient as a function of N are random as shown in Table 5, which is consistent with previously reported results [15].

$${\mathit{Nu}}_{\mathit{gp}}=0.003{{\mathit{Re}}_p}^{1.28};100<{\mathit{Re}}_p<250;R^{\mathit{2}}=0.95$$E29

or by rearranging terms as,

$$h_{\mathit{gp}}=0.003\frac{k_g}{D_p}{\left(\frac{{\rho }_g{\mathit{UD}}_p}{{\mu }_g}\right)}^{1.28}$$E30

Table 5 shows the values found for the h_gp coefficient, which fluctuate between 13 and 25.7 W m⁻² K⁻¹; these values are in a range similar to that of 6 and 23 W m⁻² K⁻¹ reported by Botterill [19]. In another investigation [20], results on the drying of forest biomass particles are reported, with h_gc values in the range between 10 and 60 W m⁻² K⁻¹, to a dryer with superheated steam and operating temperatures up to 513 K. In a subsequent study by Salve et al. [21], higher h_gp coefficient values (80–220 W m⁻² K⁻¹) were found, obtained with superficial velocities as well as elevated (3–11 m s⁻¹) and using sand in the bed.

On the other hand, Table 6 shows a comparison between the values of the Nusselt number, obtained through the experimental procedure of this research, and those predicted by Eq. (29) with R² equal to 0.95. Furthermore, the experimental results have been compared with values predicted by Eq. (31) reported by Reyes and Alvarez [22] and obtained for Reynolds numbers in the range between 33 and 150.

Re	Nugp (Experimental)	Eq. (29)	Reyes and Alvarez, Eq. (31)	Zabrodsky, Eq. (32)	Lykov, Eq. (33)	Rao and Sen Gupta, Eq. (34)
102	1.33	1.12	1.31	1.67	0.42	0.13
103	1.1	1.13	1.33	1.69	0.43	0.13
124	1.26	1.43	1.76	2.22	0.50	0.17
124	1.39	1.43	1.76	2.22	0.50	0.17
136	1.57	1.61	2.03	2.54	0.54	0.20
134	1.5	1.58	1.98	2.49	0.53	0.20
148	2	1.80	2.31	2.87	0.58	0.23
150	1.6	1.83	2.36	2.93	0.59	0.24
256	3.52	3.63	5.31	6.40	0.92	0.56
257	3.9	3.65	5.34	6.43	0.92	0.56

Table 6.

Nusselt number: comparison of experimental values with the proposed equation and correlations from other authors.

$${\mathit{Nu}}_{\mathit{gp}}=0.00116{\mathit{Re}}_p^{1.52}$$E31

The comparison is also made with Eq. (32) from Zabrodsky and Eq. (33) by Lykov, respectively, both reported in Ciesielczyk [15].

$${\mathit{Nu}}_{\mathit{gp}}=0.00195{\mathit{Re}}_p^{1.46}$$E32

$${\mathit{Nu}}_{\mathit{gp}}=0.0087{\mathit{Re}}_p^{0.84}$$E33

Finally, the results are compared with Eq. (34) from Rao and Sen Gupta and reported by Vyas and Nageshwar [23] with the Reynolds numbers in the range between 7 and 20.

$${\mathit{Nu}}_{\mathit{gp}}=0.000075{\mathit{Re}}_p^{1.61}$$E34

Of these correlations, those that are closest to Eq. (29) and the experimental values of this study are those of Reyes and Alvarez and that of Zabrodsky, Eqs. (31) and (32), respectively. The Rao and Sen Gupta equation is the one with the most deviations and is attributed to the fact that it is obtained for a very low range of the Reynolds number.

4.2.3 Convective mass transfer coefficient

The experimental values of the convective coefficient of mass transfer under the conditions already established are shown in Table 7. As in the phenomenon of heat transfer, it is verified that the rotation speed of the mechanical stirrer does not affect the mass transfer.

Rep	Shgp (experimental)	Eq. (31)	Froessling, Eq. (6)	Ranz and Marshall, Eq. (7)	Richardson and Szekely, Eq. (9)
102	0.98	0.95	7.1	17.4	20.3
103	0.62	0.96	7.1	17.4	20.4
124	0.83	1.24	7.6	18.9	22.4
124	1.56	1.24	7.6	18.9	22.4
136	1.69	1.41	7.9	19.7	23.4
134	1.66	1.38	7.9	19.6	23.3
148	1.99	1.58	8.2	20.5	24.5
150	1.53	1.61	8.2	20.6	24.6
256	3.52	3.37	10.1	26.3	32.2
257	2.54	3.39	10.1	26.4	32.2

Table 7.

Sherwood number: comparison of experimental values with the proposed equation and correlations from other authors.

In Eq. (35) the correlation obtained by adjustment between the Sherwood number and the Reynolds number is shown.

$${\mathit{Sh}}_{\mathit{gp}}=1.6x10^{-3}R{e_p}^{1.38};100<{\mathit{Re}}_p<250;R^2=0.75$$E35

or:

$$k_{\mathit{gp}}=1.6x10^{-3}\frac{D_v}{D_p}{\left(\frac{{\rho }_{g}U{D}_p}{{\mu }_g}\right)}^{1.38}$$E36

Table 7 shows a comparison between the values of the Sherwood number, obtained in this research, and those predicted by Eq. (35) with a correlation R² equal to 0.75. When comparing the experimental results with Eqs. (6), (7), and (9), unlike what happens with the heat transfer mechanism, in mass transport more significant differences are seen between our results and the Sherwood number values predicted by correlations obtained by other authors. Considering also that there are great differences between correlations already reported in the literature, it can be concluded that it is a more complex phenomenon to analyze and study experimentally. This is also verified in our research on mass transfer by observing that the value of R² from Eq. (35) is lower relative to the best correlation coefficient R² obtained in Eq. (29) for heat transfer.

The above implies that the information available in the specialized literature is not necessarily sufficient to predict heat and mass transfer coefficients, formulate mathematical modeling, and develop the thermal design of particulate forest biomass drying processes.

In the analysis of the discrepancies between experimental results with the values that predict equations reported in the literature, the characteristics of the solids of each system analyzed must be taken in consideration. It is also important to keep in mind the experimental procedures to determine the differences in temperatures and vapor concentrations between the fluidizing gas and the particles and the type of flow pattern in the fluidized bed (plug flow or complete mixing).

In this particular case, the system studied corresponds to a fluidized bed of coarse type D particles of the Geldart classification [24], which forces them to be fluidized with higher fluidization velocities and Reynolds numbers, which in this research ranged between 102 and 257.

Furthermore, Geldart type D biomass particles are solids with a high tendency to agglomerate as a result of cohesion forces between them, which are generated by surface water bridges. This is confirmed in this research with the lower values obtained for the specific surface area of wet particles S_p, compared to the values obtained when they are in a condition of low humidity S_p,0 (Table 2).

Regarding the flow pattern of the fluidized bed, it can be said that a fluidized bed of biomass particles, as a result of the combination of the air flow and the effect of the mechanical agitator, it could be considered as a system with complete mixing. Thus, according to the experimental results obtained on the QF fluidization quality index and temperature profiles inside the bed.

5. Conclusions

In an experimental equipment for drying particles in a fluidized bed, this research carries out experimental studies on the fluodynamic behavior of wet forest biomass particles suspended with a flow of hot gas in a fluidized bed with a mechanical stirrer. In addition, the biomass drying process and the heat and mass transfer mechanisms at the gas-particle interface are analyzed.

It is shown that the agitation has an important effect on the biomass particle aerodynamics if the particles have high moisture contents. The effect of the agitator is not relevant when fluidizing low moisture particles.

A methodology for the calculation of the biomass particle surface area is proposed based on Ergun equation. For the prediction of the U_mf velocity, a new correlation is also proposed, which allows fitting the experimental values with ±15% deviations in the predictions of U_mf for dry as well as wet particles.

On the other hand, the convective heat transfer coefficient between the gas and the solids was experimentally determined, varying between 13 and 25.7 W m⁻² K⁻¹. Based on a mass balance and on the experimental determination of the drying rates, the mass transfer coefficient was obtained, which varied between 6 × 10⁻³ and 20 × 10⁻³ m s⁻¹.

Thus, a correlation between the Nusselt number and the Reynolds number is proposed for the calculation of the heat transfer coefficient and a correlation between the Sherwood number and the Reynolds number for calculations of the mass transfer coefficient.

Acknowledgments

This research was financially supported by the Universidad Austral de Chile and the Universidad de Valladolid in Spain.

Nomenclature

A	cross section of the empty bed, m^2
Ap	superficial area of an arbitrary particle, m^2
cv	moisture concentration in the air, kg m^−3
cv,i	moisture concentration in the air at the entrance of the bed, kg m^−3
cv,o	moisture concentration in the air at the exit of the bed, kg m^−3
cv,s	moisture concentration in the air on the particle surface, kg m^−3
cv,∞	moisture concentration in the air outside the boundary layer, kg m^−3
Cg	gas heat capacity, J kg^−1 K^−1
dp	particle size according to the sieving method, m
Dp	diameter of the equivalent-volume sphere, m
Dv	diffusivity of the vapor in the air, m^2 s^−1
D0	reference particle diameter, m
g	acceleration due to gravity, m s^−2
G	fluid mass velocity, kg s^−1 m^−2
hfg	water heat of vaporization, J kg^−1
hgp	heat transfer coefficient at the gas-particle interface, W m^−2 K^−1
kg	thermal conductivity of the gas, W m^−1 K^−1
kgp	mass transfer coefficient at the gas-particle interface, m s^−1
l	height in the fluidized bed, from the distributor, m
L	bed height, m
${\dot{m}}_{\mathit{da}}$	dry air mass flow rate in the bed, kg s^−1.
${\dot{m}}_v$	water vapor flow rate between the solid and the gas, kg s^−1.
N	agitation speed, rev s^−1
p	pressure, Pa
S	particle surface area per unit bed volume, m^2 m^−3
Sp,0	particle surface area per unit volume of dry solids, m^2 m^−3
Sp	particle surface area per unit volume of solids, m^2 m^−3
t	time, s
T	temperature, °C
Tg	gas temperature, °C
Tg,i	inlet gas temperature in the bed, °C
Tg,o	outlet gas temperature in the bed, °C
Tg,l	temperature of the gas in the bed at a height l, °C
Tp,s	particle surface temperature, °C
Twb	wet bulb temperature, °C
U	superficial velocity, m s^−1
Umf	minimum fluidization velocity, m s^−1
va	specific volume of moist air, m^3 kg^−1
Vp	particle volume, m^3
w	moisture content in the biomass d.b., kg kg^−1
wah	humidity ratio of moist air d.b., kg kg^−1
W	particles weight in the bed, N
Δcml	logarithmic-mean difference of concentration of vapor in moist air, kg m^−3
Δp	bed pressure drop, Pa
ΔTml	logarithmic-mean temperature difference, K
ε	porosity of bed, m^3 m^−3
μg	absolute viscosity of the gas, N s m^−2
ρb	bed density, kg m^−3
ρg	gas density, kg m^−3
ρp	biomass particle density, kg m^−3
ρp,0	dry particles density, kg m^−3
ϕ	sphericity
Ga	Galileo number, Dp^3ρg^2 g /μg^2
Mρ	density ratio, ρp/ρg - 1
Nugp	Nusselt number, hgp Dp/kg
Prg	gas Prandtl number, Cg μg/kg
Rep	Reynolds number, ρg U Dp/μg
Scg	gas Schmidt number, μg/ρg Dv
Shgp	Sherwood number, kgp Dp/Dv